Homoclinic and heteroclinic orbits in a modified Lorenz system

Zhong Li; Guanrong Chen; Wolfgang A. Halang

doi:10.1016/j.ins.2003.06.005

Homoclinic and heteroclinic orbits in a modified Lorenz system

Zhong Li, Guanrong Chen, Wolfgang A. Halang

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

38 Citations (Scopus)

Abstract

This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems. © 2003 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	235-245
Journal	Information Sciences
Volume	165
Issue number	3-4
DOIs	https://doi.org/10.1016/j.ins.2003.06.005
Publication status	Published - 19 Oct 2004

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title = "Homoclinic and heteroclinic orbits in a modified Lorenz system",

abstract = "This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems. {\textcopyright} 2003 Elsevier Inc. All rights reserved.",

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T1 - Homoclinic and heteroclinic orbits in a modified Lorenz system

AU - Li, Zhong

AU - Chen, Guanrong

AU - Halang, Wolfgang A.

PY - 2004/10/19

Y1 - 2004/10/19

N2 - This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems. © 2003 Elsevier Inc. All rights reserved.

AB - This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems. © 2003 Elsevier Inc. All rights reserved.

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U2 - 10.1016/j.ins.2003.06.005

DO - 10.1016/j.ins.2003.06.005

M3 - RGC 21 - Publication in refereed journal

SN - 0020-0255

VL - 165

SP - 235

EP - 245

JO - Information Sciences

JF - Information Sciences

IS - 3-4

ER -

Homoclinic and heteroclinic orbits in a modified Lorenz system

Abstract

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